In modern communication transmitter digital information is converted to analog information and then transmitted over a channel. The digital information can include a sequence of samples that is provided at a symbol rate, i.e. adjacent samples are spaced apart by a symbol period.
In Code Division Multiple Access (CDMA) communication systems, this sequence of samples is referred to as a chip sequence and the rate with which the chips of the chip sequence are is called a chip rate. Thus, adjacent chips are said to be spaced apart by a chip period.
In CDMA communication systems the chip sequence is pulse-shaped by a pulse shaping filter (such as a Root Raised Cosine filter) to provide pulse shaped signals. The pulse shaped signals are transmitted over a medium (such as a multipath fading channel).
The pulse shaping can widen the spectrum of the chip sequence. Noise can be added to the transmitted pulsed shaped signals and timing errors can be introduced to the transmitted pulsed shaped signals.
A receiver can include one or more input antennas for receiving the transmitted pulsed shaped signals. The transmitted pulsed shaped signals (as well as added noise) can be regarded as input signals of the receiver. The input signals are filtered by one or more front end filter of the receiver, sampled to provide input signal samples and then sent to an equalizer.
The equalizer outputs equalized samples that can be further processed by the receiver. The additional processing can include descrambling, de-spreading, decoding and the like.
Linear equalizers based on minimum square error (LMMSE) criterion were recently adopted as baseline equalizers for Code Division Multiple Access (CDMA) based on third generation (3G) communication networks.
There are two families of LMSSE equalizers—fractionally spaced equalizers and symbol spaced equalizers.
In non-CDMA communication systems fractionally spaced equalizers receive oversampled input signal samples—input signal samples that were obtained by sampling the input signals at a sampling rate that is higher than the symbol rate. Adjacent oversampled input samples are spaced apart by a fraction of the symbol period.
In CDMA communication systems fractionally spaced equalizers receive oversampled input signal samples—input signal samples that were obtained by sampling the input signals at a sampling rate that is higher than the chip rate. Adjacent oversampled input samples are spaced apart by a fraction of the chip period.
In CDMA communication systems the taps of fractionally spaced equalizers are spaced apart by a fraction of the chip period of the chip sequence. In non-CDMA communication systems the taps of fractionally spaced equalizers are spaced apart by a fraction of the symbol period. The oversampling fulfills the Nyquist criterion and fractionally spaced equalizers are therefore insensitive to the sampling time at the receiver.
One drawback of fractionally spaced equalizer is their complexity and their high power consumption.
In non-CDMA communication systems symbol spaced equalizers receive symbol rate samples of the received input signal. The taps of symbol spaced equalizers are spaced apart by the symbol period.
In CDMA communication systems symbol spaced equalizers receive chip rate samples of the received input signal. The taps of chip spaced equalizers are spaced apart by the chip period.
Due to the pulse shaping applied by the transmitter the sampling does not fulfill the Nyquist criterion and symbol spaced equalizers are sensitive to the sampling time at the receiver.
In contrary to fractionally spaced equalizers, symbol spaced equalizers are simple and their power consumption is relatively low.